Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement...

Consider the initial-boundary value problem of the linear wave equation wtt − wxx = 0 on an interval. The boundary condition at the left endpoint is linear homogeneous, injecting energy into the system, while the boundary condition at the right endpoint has cubic nonlinearity of a van der Pol type. We show that the interactions of these linear and nonlinear boundary conditions can cause chaos t...

In this paper we examine a very simple and elegant example of high-dimensional chaos in a coupled array of flows in ring architecture that is cyclically symmetric and can also be viewed as an N-dimensional spatially infinite labyrinth (a "hyperlabyrinth"). The scaling laws of the largest Lyapunov exponent, the Kaplan-Yorke dimension, and the metric entropy are investigated in the high-dimension...

This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their ‘beliefs’ in each period in a boundedly rational way, according to a ‘fitness measure’ such as past realized profits. Price fluctuations are thus driven by an evolutionary dynami...

We present a detailed investigation of the rich variety of bifurcations and chaos associated with a very simple nonlinear parallel nonautonomous LCR circuit with Chua’s diode as its only nonlinear element as briefly reported recently [Thamilmaran et al., 2000]. It is proposed as a variant of the simplest nonlinear nonautonomous circuit introduced by Murali, Lakshmanan and Chua (MLC) [Murali et ...

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two paramet...

This paper examines the most probable route to chaos in high-dimensional dynamical systems function space (time-delay neural networks) endowed with a probability measure in a computational setting . The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of Neimark-Sacker bifurcations into chaos. The a...

To construct generalized Lorenz systems, higher-order modes in doubled Fourier expansions of a stream function and temperature variations must be considered. Selection of these modes is guided by the requirements that they conserve energy in the dissipationless limit and lead to systems that have bounded solutions. The previous study showed how to select the modes by using either vertical or ho...

We study the bifurcations of a ducted two-dimensional premixed flame using numerical simulations of the coupled dynamical system. When the flame position in the duct is changed the system undergoes transition to period-1, quasi-periodic, period-2, frequencylocked and chaotic oscillations via different bifurcations. For certain parameter ranges multiple stable solutions exist and the ultimate st...